Refraction through a Rectangular Glass Slab

& The Refractive IndexBy,

Team members

Sharanraj(Captain)

Sri Ram(Vice-Captain) Adhith

Dhiraj Vyshakh Buvaneshwar

What is Refraction?Refraction is the change in direction of propagation of

a wave due to a change in its transmission medium.

Laws of Refraction

When light travels from one medium to another, it generally bends, or refracts. The law of  refraction gives us a way of predicting the amount of bend. This law is more complicated than that for reflection, but an understanding of refraction will be necessary for our future discussion of lenses and their applications. The law of refraction is also known as Snell's law, named for Willobrord Snell, who discovered the law in 1621.

Snell's law gives the relationship between angles of incidence and refraction for a wave impinging on an interface between two media with different index of refraction. The law follows from the boundary condition that a wave be continuous across a boundary, which requires that the phase of the wave be constant on any given plane, resulting in

Laws of Refraction

When we talk about the speed of light, we're usually talking about the speed of light in a vacuum, which is 3.00 x 108 m/s. When light travels through something else, such as glass, diamond, or plastic, it travels at a different speed. The speed of light in a given material is

Refraction

related to a quantity called the index of refraction, n, which is defined as the ratio of the speed of light in vacuum to the speed of light in the medium:index of refraction : n = c / v , where the speed of light in a medium is v and c is the speed of light in vacuum.

Rules of RefractionRule-1 : When a

light ray travels from a rarer medium to a denser medium, the light ray bends towards the normal.

Rule-2 : When a light ray travels from a denser medium to a rarer medium, the light ray bends away from the normal. 

Some examples of refraction around us  1)  If you place a pencil in a glass

of water, you will see that the pencil appears to be bent. Now, you know for a fact that the pencil is not bent at all, it just appears to be so. This is the effect of light. Light is actually a form of energy called electromagnetic radiation. There is a wide spectrum of radiation with X-rays, ultraviolet rays, infrared rays etc. and most of them are present in the atmosphere with their own definite wavelengths and properties, but the only wavelengths that we are able to see is that of Visible Light. (Fig 1)

Fig 1

Since light is in the form of aves, it has many characteristic properties like reflection (this helps us to see objects, because only when light reflects off an object, we can see it), travels at different speeds in different objects and most importantly, undergoes refraction. 2) The term refraction is defined as the bending of light as it passes from one type of material into another. Because light travels at different speeds in the two materials, it changes its speed at the boundary of the two materials. If a beam of light hits this boundary at an angle, then light hitting the side first will be forced to slow down or speed up before light on the other side hits the new material. This causes the beam to bend, or refract, at the boundary. Suppose we were to place a coin in a glass of water. The light bouncing off the coin underwater, for instance, would have to first travel through the water and then the air to reach an observer's eye.  At the boundary, it gets refracted and reaches the observer's eye, thus appearing to be slightly raised. (Fig 2)

Fig 2

Refraction by practical methodApparatus:

A drawing board, rectangular glass slab, office pins, sheet of white paper, a protractor and sharply pointed pencil.

About the experiment:

Materials Req.: A rectangular slab of glass, a laser pointer, a few sheets of paper, a sharp pencil, a ruler, and a protractor.

PQRS represents a glass slab. Consider that a ray of light enters the glass slab along AE. It means that light is travelling from a rarer medium (i.e., air) to glass which is denser medium. Thus the refracted ray bends towards the normal making r<i. 

At the other face of the slab, the ray EF while travelling through glass meets the surface SR of air which is a rarer medium . It emerges out along FD ,bending away from the normal.The ray FD is known as the emergent ray . 

The angle which the emergent ray makes with the normal at the point of emergence is called the angle of emergence and is denoted by the letter E

Fix a sheet of white paper on a drawing board with drawing pins. Place the given glass slab nearly in the middle of the sheet.

Mark the boundary of the glass slab with a sharp pencil and label it as PQRS after removing the slab from its position.

On the line PQ mark a point E and draw a normal N1EN2 at it. Draw a line AE making angle AEN1 with the normal.The angle should neither too small nor too large (say about 40 degree).

Now place the glass slab again on its boundary PQRS and fix two pins A and B vertically about 10 cm apart on the line AE (say points A and B).

Look through the glass slab along the plane of the paper from the side SR and move your head until the images of the two pins A and B are seen clearly. Closing your one eye ,adjust the position of your head in such a way that the images of the pins A and B lie in the same straight line.

Procedure :

Fix two other pins C and D vertically in such a way that the images of the pins A and B and pins C and D, all these four, lie in the same straight line. Ensure that the feet of the pins ( not their heads ) lie in the same straight line.

Remove the slab and also the pins from the board and encircle the pin-pricks on the paper,with a sharp pencil.

Join the points D and C and produce the line DC towards the slab so that it meets the boundary line RS at the point F. Join the points e and F. Thus for the incident ray represented by line AE, the refracted ray and the emergant ray are represented by EF and FD respectively.

On the line RS draw a normal N1'FN2'  at point F. Now, with a protractor, measure angle AEN1, angle FEN2 and angle DFN2' labelled as angle i, angle r and angle e respectively. 

Now place the glass slab at some other position on the sheet of paper fixed on the board and repeat all the above steps again taking another angle of incidence.

Measure the angle of incidence i.e angle of refraction, angle of emergence, again.

Make a record of your observations in the observation table as shown below.

Observation Table :

History of the Refractive Index

Thomas Young

Thomas Young was presumably the person who first used, and invented, the name "index of refraction", in 1807. At the same time he changed this value of refractive power into a single number, instead of the traditional ratio of two numbers. The ratio had the disadvantage of different appearances. Newton, who called it the "proportion of the sines of incidence and refraction", wrote it as a ratio of two numbers, like "529 to 396" (or "nearly 4 to 3"; for water). Hauksbee, who called it the "ratio of refraction", wrote it as a ratio with a fixed numerator, like "10000 to 7451.9" (for urine). Hutton wrote it as a ratio with a fixed denominator, like 1.3358 to 1 (water).

Young did not use a symbol for the index of refraction, in 1807. In the next years, others started using different symbols: n, m, and µ. The symbol n gradually prevailed.

The Refractive IndexIn optics the refractive index or index of refraction n of an optical medium is adimensionless number that describes how light, or any other radiation, propagates through that medium. It is defined as

where c is the speed of light in vacuum and v is the phase velocity of light in the medium.

A ray of light that travels obliquely from one transparent medium into another will change its direction in the second medium. The extent of the change in direction that takes place in a given pair of media is expressed in terms of the refractive index, the “constant” appearing on the right-hand scale of Eq. ,

sin i / sin r = constant . The refractive index can be linked to an important

physical quantity, the relative speed of propagation of light in different media. It turns out that light propagates with different speeds in different media. Light travels the fastest in vacuum with the highest speed of 3.108ms-1. In air, the speed of light is only marginally less, compared to that in vacuum. It reduces considerably in glass or water. The value of the refractive index for a given pair of media, as given below.

Consider a ray of light travelling from medium 1 into medium 2, as shown in the fig 4. Let v1 be the speed of the light in medium v2 be the speed of light in medium 2. The refractive index of medium 2 with respect to medium 1 is given by the ratio of the speed of light in medium 1 and the speed of light in medium 2. This is usually represented by the symbol n21.

This can be expressed in an equation form as

Fig 4

n21 = Speed of light in medium 1 / Speed of light in medium 2 = v1 / v2

By the same argument,the refractive index of medium 1 with respect to medium 2 is represented as n12.. It is given by,

n12 = Speed of light in medium 2 / Speed of light in medium 1 = v2 / v1 If medium 1 is vacuum or air, then the refractive index of

medium 2 is considered with respect to vacuum. This is called the absolute refractive index of the medium. It is simply represented as n2. . If c is the speed of light in air and v is the speed of light in the medium, then, the refractive index of the medium nm is given by

nm = Speed of light in air / Speed of light in the medium = c / v The absolute refractive index of a medium is simply

called its refractive index. The refractive index of several media is given in Table 1. From the Table you can know that the refractive index of water, nw = 1.33. This means that the ratio of the speed of light in air and the speed of light in water is equal to 1.33. Similarly, the refractive index of crown glass, ng =1.52. Such data are helpful in many places. However, you need not memorise the data.

Table 1

Note from Table 1 that an optically denser medium may not possess greater mass density. For example, kerosene having higher refractive index, is optically denser than water, although its mass density is less than water.

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